NAEP assessments use complex sample designs to create student samples from which population and subpopulation characteristics could be estimated with reasonably high precision and low sampling variability. Student sampling weights ensure valid inferences from the student samples to their respective populations. In the 2008 long-term trend (LTT) assessment, weights were developed for students sampled at ages 9, 13, and 17 for assessments in mathematics and reading. Each student was assigned a weight to be used for making inferences about students in the target population. This weight is known as the final full-sample student weight. The final full-sample weight contains five components:

the base weight,

school nonresponse adjustments,

student nonresponse adjustments,

school weight trimming adjustments, and

student weight trimming adjustments.

The base weight is the inverse of the overall probability of selecting a student and assigning that student to a particular assessment. The sample design that determines the base weights is discussed in the NAEP 2008 LTT sample design section.

The base weight is adjusted for two sources of nonparticipation: school level and student level. These weighting adjustments seek to reduce the potential for bias from such nonparticipation by

increasing the weights of students from schools similar to those schools not participating, and

increasing the weights of participating students similar to those students from within participating schools who did not attend the assessment session (or makeup session) as scheduled.

Furthermore, the final weights reflect the trimming of extremely large weights at both the school and student levels. These weighting adjustments seek to reduce variances of survey estimates.

In addition to the final full-sample weight, a set of replicate weights was provided for each student. These replicate weights are used to calculate the variances of survey estimates using the jackknife repeated replication method. The methods used to derive these weights were aimed at reflecting the features of the sample design, so that when the jackknife variance estimation procedure is implemented, approximately unbiased estimates of sampling variance are obtained. In addition, the various weighting procedures were repeated on each set of replicate weights to appropriately reflect the impact of the weighting adjustments on the sampling variance of a survey estimate.

Quality control checks were carried out throughout the weighting process to ensure the accuracy of the full-sample and replicate weights.